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De Broglie wavelength calculator
Nuclear and particles
The wavelength associated with a moving particle.
λ = h / (m v)
This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.
Quantity to find
Working
- Write the equationλ = h / (m v)
- Constants usedh = 6.63 × 10−34 J s
- Substitute the valuesλ = (6.63 × 10−34) ÷ ((9.11 × 10−31) × (3 × 106))
- Calculateλ = 2.42591 × 10−10 m
- Give the answer to 3 significant figuresλ = 2.43 × 10−10 m
Worked example
Find λ, the de Broglie wavelength. Given: mass m = 9.11 × 10⁻³¹ kg; speed v = 3.00 × 10⁶ m/s; Planck constant h = 6.63 × 10⁻³⁴ J s.
- Write the equationλ = h / (m v)
- Constants usedh = 6.63 × 10−34 J s
- Substitute the valuesλ = (6.63 × 10−34) ÷ ((9.11 × 10−31) × (3 × 106))
- Calculateλ = 2.42591 × 10−10 m
- Give the answer to 3 significant figuresλ = 2.43 × 10−10 m
Symbols and units
| Symbol | Quantity | SI unit |
|---|---|---|
| λ | De Broglie wavelength | m |
| h | Planck constant (constant) | J s |
| m | Mass | kg |
| v | Speed | m/s |
De Broglie wavelength: rearranged
- To find de Broglie wavelength: λ = h / (m v)
- To find mass: m = h / (λ v)
- To find speed: v = h / (λ m)
Exam tip
For electrons, m = 9.11 × 10⁻³¹ kg. The wavelength of everyday objects is far too small to notice.
Common questions
What is the formula for de broglie wavelength?
The equation is λ = h / (m v), where λ is the de Broglie wavelength (m); m is the mass (kg); v is the speed (m/s); h is the Planck constant (J s).
What units should I use for de broglie wavelength?
In SI units: de Broglie wavelength in m, Planck constant in J s, mass in kg, speed in m/s. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.
How do I rearrange λ = h / (m v)?
Rearranging gives these forms: to find de Broglie wavelength: λ = h / (m v). to find mass: m = h / (λ v). to find speed: v = h / (λ m).
Practise de broglie wavelength questions
Press the button for a question with random numbers. Work it out on paper first, then type your answer.
Related
Read the full explanation on the de Broglie wavelength formula page. More nuclear and particles equations: Photon energy, Photon energy from wavelength, Photoelectric equation, Radioactive decay and half-life, Activity and decay constant, Half-life and decay constant, Mass–energy equivalence. See the full list on the a-level physics equation calculator page.